Mathematics Grade 11 P2 North West June 2017 Question Paper

GRADE 11 MATHEMATICS EXAMINATION P2 JUNE 2017 MARKS: 100 TIME: 2 hours This question paper consists of 9 printed pages and 6 diagram sheets.

Mathematics / P2 NCS – Grade 11 NW/June 2017 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 6 questions. 2. Answer ALL the questions. 3. Number the answers correctly according to the numbering system used in this question paper 4. Clearly show ALL calculations, diagrams, graphs, et cetera which you have used in determining your answers. 5. Answers only will not necessarily be awarded full marks. 6. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 7. If necessary, answers should be rounded off to TWO decimal places, unless stated otherwise. 8. Diagrams are NOT necessarily drawn to scale. 9. Write neatly and legibly. 2

Mathematics / P2 NCS – Grade 11 NW/June 2017 QUESTION 1 In the diagram below A (0; 11), B(10;11) and C(16;3) are the vertices of ABC, with height CD . y A 0;11 B 10;11 D M C 16;3 x 0 1.1 Write down the length of the line AB. (1) 1.2 Show that is isosceles. (3) 1.3 Write down the coordinates of the point D. (2) 1.4 Calculate the area of ∆ ABC. (3) 1.5 Determine the coordinates of M, the midpoint of AC. (2) 1.6 Determine the gradient of AC. (2) 1.7 Show that BMCD is a cyclic quadrilateral. (5) [18] 3

Mathematics / P2 NCS – Grade 11 NW/June 2017 QUESTION 2 2.1 If 5cos A + 3 = 0 and 180° < A < 360° , without using a calculator and with the aid of a diagram, determine the value of 2.1.1 (4) 2.1.2 (2) 2.2 If WITHOUT using a calculator, determine the following in terms of 2.2.1 (2) 2.2.2 (3) 2.3 Prove that (4) [15] QUESTION 3 3.1 Simplify fully WITHOUT the use of a calculator: (6) 3.2 Determine the general solution of the equation: (6) [12] 4

Mathematics / P2 NCS – Grade 11 NW/June 2017 QUESTION 4 Sketched below are the graphs of and 4.1 Determine the values of and (4) 4.2 Write down the period of f. (1) 4.3 If write down the amplitude of h. (1) 4.4 Calculate the values of x for which for (Show all your calculations) (5) 4.5 Determine the value(s) of x for which g will decrease while f increases for . (2) [13] 5

Mathematics / P2 NCS – Grade 11 NW/June 2017 QUESTION 5 5.1 In the diagram below the circle with centre O passes through L, N and P. KLM is a tangent to the circle at L. NP, NL and LP are joined. N O P  x K L M Using the above diagram, prove the theorem that states that . (5) 6

Mathematics / P2 NCS – Grade 11 NW/June 2017 5.2 In the diagram below, O is the centre of circle TRNM. RT produced meets tangent MP at P. OM intersect TN at K. K is the midpoint of TN. 5.2.1 Calculate, stating reasons, the size of: (a) (2) (b) (2) (c) (4) 5.2.2 Prove that TN // PM. (3) 5.2.3 Calculate the length of KM. (3) [19] 7

Mathematics / P2 NCS – Grade 11 NW/June 2017 QUESTION 6 6.1 Complete the following statements so that they are true: 6.1.1 If a chord of a circle subtends a right angle on the circumference, then (1) the chord is a … 6.1.2 Opposite interior angles of a cyclic quadrilateral are … (1) 6.2 In the diagram below, two circles have a common tangent TAB.PT is a tangent to the smaller circle.PAQ, QRT and NAR are straight lines. Let Q ^ = 40 ° . 6.2.1 Determine, with reasons, THREE other angles equal to 40°. (5) 6.2.2 P1 = ^ If ^ A 4 prove that PTRN is a parallelogram. (5) 6.3 Tangent BC touches the circle ABDE at B. Chords AD and BE intersect at F. ^ 1=x and Chord ED is produced to C. AB || EC. It is further given that B A 1= y . ^ 8

Mathematics / P2 NCS – Grade 11 NW/June 2017 6.3.1 Determine the size of C ^ in terms of x and y. (6) 6.3.2 Becky says that BCDF is not a cyclic quadrilateral while Teboho insists that it is. Who is correct? Show all your working and reasons in determining your answer. (5) [23] TOTAL : 100 NAME: ………………………………………. CLASS: ……….. DIAGRAM SHEET 1 QUESTION 1 9

Mathematics / P2 NCS – Grade 11 NW/June 2017 y A 0;11 B 10;11 D M C 16;3 x 0 NAME: ………………………………………. CLASS: ……….. DIAGRAM SHEET 2 10

Mathematics / P2 NCS – Grade 11 NW/June 2017 QUESTION 4 NAME: ………………………………………. CLASS: ……….. 11

Mathematics / P2 NCS – Grade 11 NW/June 2017 DIAGRAM SHEET 3 QUESTION 5.1 N O P x K L M NAME: ………………………………………. CLASS: ……….. 12

Mathematics / P2 NCS – Grade 11 NW/June 2017 DIAGRAM SHEET 4 QUESTION 5.2 NAME: ………………………………………. CLASS: ……….. 13

Mathematics / P2 NCS – Grade 11 NW/June 2017 DIAGRAM SHEET 5 QUESTION 6.2 NAME: ………………………………………. CLASS: ……….. 14

Mathematics / P2 NCS – Grade 11 NW/June 2017 DIAGRAM SHEET 6 QUESTION 6.3 A 1 B 1 11 1 1 F C D E 15